How do you find the equation of line L that passes through the points (1,3) and (-3,4)?

2 Answers
Feb 6, 2015

The answer is: #y=-1/4x+13/4#.

It is possible to use this formula, that is the formula to find a line given two points #A(x_A,y_A)# and #B(x_B,y_B)#:

#(y-y_A)/(y_B-y_A)=(x-x_A)/(x_B-x_A)#.

So:

#(y-3)/(4-3)=(x-1)/(-3-1)rArry-3=-1/4(x-1)rArr#

#y=-1/4x+1/4+3rArry=-1/4x+13/4#.

Feb 7, 2015

I created a video that answers the question and shows you how to check you work.
http://www.frontporchmath.com/topic/equation-of-a-line-question-1/

To solve this problem you first find the slope of the line, using the two points #(1,3)# and #(-3,4)#.

#(Delta y)/(Delta x) = (4 - 3)/(-3 - 1) = -1/4#

Then you use the y-intercept equation of a line using the slope above and one of the above sets of points to find the y-intercept.

#y = mx + b#
#4 = -1/4(-3) + b#
#4 = 3/4 + b#
#3 1/4 = b#

Then just plug that information into #y=mx+b#

#y= -1/4x +3 1/4#
or
#y=1/4x +(13)/4#